arXiv:2605.15240v1 Announce Type: cross
Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in kernel methods and the estimation of eigenvectors and eigenvalues of matrices, offering a more intuitive understanding compared to prior work with minimal assumptions. We also show that, since the prediction task in KRR is essentially the weighted sum of eigenvectors/singular vectors, by analyzing how much error can be caused by perturbations to the kernel matrix, we can then derive a bound on this generalization error using the estimation stability of matrix eigenvalues and eigenvectors. Compared with previous work, our analysis concentrates on finite-sample settings and on the generalization error arising from having a suboptimal finite training set. Our findings reveal that in kernel methods, as long as the kernel is of high rank, the near-zero reconstruction error can be trivially obtained, implying that the reconstruction error will have limited predictive power for generalization. Finally, we establish a generalization bound from an eigenvalues/eigenvectors estimation perspective, showing that strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between consecutive eigenvalues.
Science Journals
arXiv:2605.15225v1 Announce Type: cross
Abstract: Biologically-inspired AI agent frameworks claim reliability benefits through structural guarantees adapted from gene regulatory networks, immune systems, and metabolic control. These claims are rarely tested empirically against simpler alternatives. We present three deep benchmarks: metabolic priority gating, autoinducer-based quorum sensing, and Bayesian stagnation detection, each comparing a biologically-grounded implementation against a naive non-biological alternative and an ablated control, across 1,000 trials per seed and 10 seeds (10M+ data points total).
arXiv:2605.12581v1 Announce Type: cross
Abstract: Synthesising autonomous agents that can navigate uncertain environments while adhering to complex temporal constraints remains a fundamental challenge. While Linear Temporal Logic (LTL) provides a rigorous language for specifying such tasks, the inherent undecidability of qualitatively verifying LTL satisfaction in partially observable Markov decision processes renders quantitative synthesis difficult, especially when designing reliable reward signals for approximate solvers. In this paper, we bridge this gap with a novel, sound reward-shaping mechanism that dynamically generates belief-dependent rewards grounded in certified LTL satisfaction. By integrating this mechanism into an enhanced Monte Carlo Planning framework, we empower agents to navigate the `fog' of partial observability with a search process focused on maximising verifiable success. Our experiments demonstrate that this approach not only thrives in scenarios where existing solvers fail but also maintains effectiveness and scalability across diverse benchmark domains.
arXiv:2605.06475v1 Announce Type: cross
Abstract: We introduce a probabilistic approach for dating historical manuscript pages from visual features alone. Instead of aggregating centuries into classes as is standard in the previous literature, we pose dating as an evidential deep regression problem over a continuous year axis, allowing our neural network to output a full predictive distribution with decomposed aleatoric and epistemic uncertainty in a single forward pass. Our architecture combines an EfficientNet-B2 backbone with a Normal-Inverse-Gamma (NIG) output head trained with a joint negative-log-likelihood and evidence-regularization objective. On the DIVA-HisDB benchmark (150 pages, 3 medieval codices, 151,936 patches), our model scores a test MAE of 5.4 years, well below the 50-year century-label supervision granularity, with 93\% of patches within 5 years and 97\% within 10 years. Our approach achieves \textbf{PICP=92.6\%}, the best calibration among all compared methods, in a single forward pass, outperforming MC Dropout (PICP=88.2\%, 50 passes) and Deep Ensembles (PICP=79.7\%, 5 models) at $5\times$ lower inference cost. Uncertainty decomposition shows aleatoric uncertainty is a strong predictor of dating error (Spearman $\rho=0.729$), and a selective prediction about the most certain 20\% of patches can provide \textbf{0.5 years MAE}. We show that predicted uncertainty increases as image degradation worsens, spatial decomposition maps explain which script regions cause aleatoric uncertainty, and page-level aggregation reduces MAE to 4.5 years with $\rho=0.905$ between uncertainty and page-level error.
arXiv:2604.24135v1 Announce Type: cross
Abstract: The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where points share an edge if they differ by one in one coordinate.
We give an algorithm, that for two simple paths on $n$ vertices, $(1+\varepsilon)$-approximates the Fr\'echet distance in time $\widetilde{O}((\frac{n}{\varepsilon})^{2-2/d} +n)$. We complement this by a near-matching fine-grained lower bound: for constant dimensions $d \geq 3$, there is no $O((\varepsilon^{2/d}(\frac{n}{\varepsilon})^{2-2/d})^{1-\delta})$ algorithm for any $\delta>0$ unless the Orthogonal Vector Hypothesis fails. Thus, our results are tight up to a factor $\varepsilon^{2/d}$ and $\log(n)$-factors. We extend our results to imbalanced lower and upper bounds, where the curves have $n$ and $m$ vertices respectively, and also obtain near-tight bounds.
Driemel, Har-Peled and Wenk [DCG'12] studied \emph{realistic assumptions} for curves to speed up Fr\'echet distance computation. One of these assumptions is $\lambda$-low density and they can compute a $(1+\varepsilon)$-approximation between $\lambda$-low dense curves in time $\widetilde{O}( \varepsilon^{-2} \lambda^2 n^{2(1-1/d)})$. By adapting our lower bound, we show that their algorithm has a tight dependency on $n$ and a tight dependency on $\varepsilon$ as $d$ goes to infinity. A gap remains in terms of $\lambda$.
arXiv:2602.08843v1 Announce Type: cross
Abstract: Many fundamental problems in computational geometry admit no algorithm running in $o(n \log n)$ time for $n$ planar input points, via classical reductions from sorting. Prominent examples include the computation of convex hulls, quadtrees, onion layer decompositions, Euclidean minimum spanning trees, KD-trees, Voronoi diagrams, and decremental closest-pair.
A classical result shows that, given $n$ points sorted along a single direction, the convex hull can be constructed in linear time. Subsequent works established that for all of the other above problems, this information does not suffice. In 1989, Aggarwal, Guibas, Saxe, and Shor asked: Under which conditions can a Voronoi diagram be computed in $o(n \log n)$ time? Since then, the question of whether sorting along TWO directions enables a $o(n \log n)$-time algorithm for such problems has remained open and has been repeatedly mentioned in the literature.
In this paper, we introduce the Presort Hierarchy: A problem is 1-Presortable if, given a sorting along one axis, it permits a (possibly randomised) $o(n \log n)$-time algorithm. It is 2-Presortable if sortings along both axes suffice. It is Presort-Hard otherwise. Our main result is that quadtrees, and by extension Delaunay triangulations, Voronoi diagrams, and Euclidean minimum spanning trees, are 2-Presortable: we present an algorithm with expected running time $O(n \sqrt{\log n})$. This addresses the longstanding open problem posed by Aggarwal, Guibas, Saxe, and Shor (albeit randomised). We complement this result by showing that some of the other above geometric problems are also 2-Presortable or Presort-Hard.
arXiv:2509.22151v3 Announce Type: cross
Abstract: Material node graphs are programs that generate the 2D channels of procedural materials, including geometry such as roughness and displacement maps, and reflectance such as albedo and conductivity maps. They are essential in computer graphics for representing the appearance of virtual 3D objects parametrically and at arbitrary resolution. In particular, their directed acyclic graph structure and intermediate states enable a modular, interpretable workflow for interactive appearance modeling. However, creating such graphs remains challenging and typically requires professional training. While recent neural program synthesis approaches attempt to simplify this process, they solely represent graphs as textual programs, failing to capture the inherently visual-spatial nature of node graphs that makes them accessible to humans. To address this gap, we present MultiMat, a multimodal program synthesis framework that leverages large multimodal models to process both visual and textual graph representations for improved generation of procedural material graphs. We train our models on a new dataset of production-quality procedural materials and combine them with a constrained tree search inference algorithm that ensures static correctness while efficiently navigating the program space. Our experimental results show that our multimodal program synthesis method is more efficient in both unconditional and conditional graph synthesis with higher visual quality and fidelity than text-only baselines, establishing new state-of-the-art performance.
arXiv:2512.14671v3 Announce Type: replace
Abstract: We introduce ART, Articulated Reconstruction Transformer -- a category-agnostic, feed-forward model that reconstructs complete 3D articulated objects from only sparse, multi-state RGB images. Previous methods for articulated object reconstruction either rely on slow optimization with fragile cross-state correspondences or use feed-forward models limited to specific object categories. In contrast, ART treats articulated objects as assemblies of rigid parts, formulating reconstruction as part-based prediction. Our newly designed transformer architecture maps sparse image inputs to a set of learnable part slots, from which ART jointly decodes unified representations for individual parts, including their 3D geometry, texture, and explicit articulation parameters. The resulting reconstructions are physically interpretable and readily exportable for simulation. Trained on a large-scale, diverse dataset with per-part supervision, and evaluated across diverse benchmarks, ART achieves significant improvements over existing baselines and establishes a new state of the art for articulated object reconstruction from image inputs.
arXiv:2605.16257v1 Announce Type: new
Abstract: Achieving human-level manipulation requires dexterous robotic hands capable of complex object interactions. Advancing such capabilities further demands standardized benchmarks for systematic evaluation. However, existing dexterous benchmarks lack tasks that reflect the unique manipulation capabilities of dexterous hands over parallel grippers, as well as comprehensive evaluation pipelines. In this paper, we present DexJoCo, a benchmark and toolkit for task-oriented dexterous manipulation, comprising 11 functionally grounded tasks that evaluate tool-use, bimanual coordination, long-horizon execution, and reasoning. We develop a low-cost data collection system and collect 1.1K trajectories across these tasks, with support for domain randomization to assess robustness. We benchmark modern models under diverse settings, including visual and dynamics randomization, multi-task training, and action-head adaptation. Through extensive empirical analysis, we identify several important insights and common limitations of current policies in dexterous manipulation, highlighting key challenges for future research in dexterous hand robot learning. Project page available at: https://dexjoco.github.io
arXiv:2605.16255v1 Announce Type: new
Abstract: Demand for AI accelerators is rapidly increasing rack power density, with projections approaching 1MW per deployment by 2027. This poses a major challenge for datacenter power delivery designers. As power densities increase, a datacenter designed for a different target density may strand power, i.e., may be unable to use all the power that its delivery hierarchy has provisioned. Designs must remain efficient over long datacenter lifetimes and multiple hardware generations. Power utilization is particularly important as grid power capacity is a scarce resource in the AI era.
Designing an efficient power delivery hierarchy for the long run is difficult because rack placement feasibility, workload impact, and cost depend jointly on electrical topology, deployment granularity, placement policy, power oversubscription, and workload mix. Moreover, each of these factors evolve over time, have inter-dependencies across multiple resource dimensions, and generally do not lend themselves to closed-form analysis.
To address this challenge, we develop a framework for evaluating datacenter power delivery designs using throughput, power, and cost metrics over realistic arrival, oversubscription, and decommissioning sequences. The framework combines projection models for GPU, compute, and storage deployments with operational factors grounded in production data from Microsoft Azure. Our results show that multi-resource stranding materially changes deployable capacity, effective capital expenditure, and delivered performance, and quantify how rising density from rack- and pod-scale AI systems shapes these outcomes. For AI datacenter design, the relevant planning objective is not installed megawatts, but deployable capacity over time.
arXiv:2605.16253v1 Announce Type: new
Abstract: Ray tracing (RT) is a 3D graphics technique that offers highly realistic visuals. It is becoming prominent and accessible as GPU vendors have integrated dedicated ray tracing acceleration hardware. However, tracing millions of rays through 3D scenes consisting of high numbers of triangles in real time is challenging and requires expensive hardware. The main bottleneck in RT workloads is the expensive Bounding Volume Hierarchy (BVH) traversal task, which is a large tree structure that encodes the 3D scene. BVH traversal is a memory-bound problem, as the GPU threads spend most of their time reading tree node data from memory. In this work, we attack the memory latency bottleneck of ray tracing through prefetching. We propose a novel hardware prefetcher, named Tree Traversal Prefetcher (TTP), for ray tracing. The main idea is to leverage the existing tree traversal stack in the RT units for highly accurate prefetching. In particular, TTP prefetches nodes using the addresses already available on the hardware traversal stacks of each thread. For DFS (Depth-first search) based traversal, prefetches are generated when nodes are being popped consecutively from the traversal stack, potentially corresponding to upward traversal through the tree. We evaluate TTP on a cycle-level simulator, Vulkan-sim 2.0, and show that it achieves 1.48x speedup on average (up to 1.89x) compared to the baseline, with nearly negligible hardware overhead. TTP achieves 98.92% average L1 accuracy, which is the ratio of the prefetched blocks being actually referenced by demand loads. The coverage, computed as the ratio of L1 miss reduction over baseline L1 misses, is 31.54%, correlating well with the achieved speedup.
arXiv:2605.16250v1 Announce Type: new
Abstract: Distribution utilities are now expected to deliver bills that customers can actually read attach a defensible carbon number to every kWh sold and schedule load against grid stress and emissions constraints We propose an end-to-end framework that unifies four production-grade capabilities under one architectural roof a generative-AI agent that drafts each customers natural-language billing statement from structured numeric inputs under a constrained decoding policy a transformer-based forecaster that supplies the day-ahead consumption estimate with calibrated quantile bands
arXiv:2605.16245v1 Announce Type: new
Abstract: Generative artificial intelligence (AI) is increasingly integrated into the online platforms where humans exchange opinions; large language models (LLMs) now polish users' posts on LinkedIn and provide context for content shared on X. While prior work has shown that AI can express biased opinions and shape individuals' opinions during human-AI interactions, less attention has been paid to its influence on collective opinion formation when mediating human-to-human communication. We address this gap via a combination of empirical and theoretical analyses. We show empirically that LLMs from multiple popular families introduce directional biases when instructed to edit human-written texts on contested topics, for example, nudging texts in favor of gun control and against atheism. Building on this observation, we introduce a mathematical model of opinion dynamics in which an AI system sits between users on a social network, transforming the opinions they express and perceive. By analytically characterizing the equilibrium of this model and performing simulations on real social network data, we show that biases introduced by AI in human-to-human communication can be amplified through the network and shift collective opinion in their direction. In light of these findings, we investigate whether such biases are controllable by online platforms. We audit the "Explain this post" feature on X and find evidence of pro-life bias in Grok's outputs on abortion-related content, which we trace back to specific design choices. We conclude with a discussion of the broader implications of our findings in relation to ongoing legislative efforts in the European Union.
arXiv:2505.24573v2 Announce Type: replace
Abstract: In this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of $ t $ symbols belong each to $ N $ local repair sets, which are pairwise disjoint after removing the $ t $ symbols, and which are of size $ r+\delta-1 $ and can correct $ \delta-1 $ erasures locally. Classical LRCs with $ N $ disjoint repair sets and LRCs with $ N $-availability are recovered when setting $ t = 1 $ and $ t=\delta-1=1 $, respectively. Allowing $ t > 1 $ enables our codes to reduce the storage overhead for the same locality and availability. In this setting, we define maximally recoverable LRCs (MR-LRCs) as those that can correct any globally correctable erasure pattern given the locality and availability constraints. We then identify a large class of global erasure patterns that can be corrected by such MR-LRCs and prove that they are all the correctable patterns when $ t=1 $. We provide three explicit constructions of LRCs that can correct such erasure patterns (thus MR-LRCs for $ t=1 $), based on MSRD codes, each attaining the smallest finite-field sizes for some parameter regime. Finally, we extend the known lower bound on finite-field sizes from classical MR-LRCs to our setting (for any value of $ t $).
arXiv:2409.03897v3 Announce Type: replace
Abstract: Large-scale multi-agent systems are often deployed across wide geographic areas, where agents interact with heterogeneous environments. There is an emerging interest in understanding the role of heterogeneity in the performance of the federated versions of classic reinforcement learning algorithms. In this paper, we study synchronous federated Q-learning, which aims to learn an optimal Q-function by having $K$ agents average their local Q-estimates per $E$ iterations. We observe an interesting phenomenon on the convergence speeds in terms of $K$ and $E$. Similar to the homogeneous environment settings, there is a linear speed-up concerning $K$ in reducing the errors that arise from sampling randomness. Yet, in sharp contrast to the homogeneous settings, $E>1$ leads to significant performance degradation. Specifically, we provide a fine-grained characterization of the error evolution in the presence of environmental heterogeneity, which decay to zero as the number of iterations $T$ increases. The slow convergence of having $E>1$ turns out to be fundamental rather than an artifact of our analysis. We prove that, for a wide range of stepsizes, the $\ell_{\infty}$ norm of the error cannot decay faster than $\Theta (E/T)$. In addition, our experiments demonstrate that the convergence exhibits an interesting two-phase phenomenon. For any given stepsize, there is a sharp phase-transition of the convergence: the error decays rapidly in the beginning yet later bounces up and stabilizes. Provided that the phase-transition time can be estimated, choosing different stepsizes for the two phases leads to faster overall convergence.
arXiv:2605.15667v1 Announce Type: cross
Abstract: On a finite outcome space, the canonical Gibbs distribution is usually obtained by maximizing Shannon entropy at fixed mean of an externally supplied energy functional. This paper studies the finite-state consequences of a ratio-cost construction instead: after adopting the normalized d'Alembert degree-two closure called the Recognition Composition Law (RCL), with unit log-curvature calibration at the reference ratio, the continuous nontrivial positive branch is $J(x)=\tfrac12(x+x^{-1})-1=\cosh(\log x)-1$. Given the induced cost vector $X_\omega=J(r_\omega)$, multinomial counting and convex duality recover the finite-state Gibbs weights and the identity $F_{\mathrm{R}}(q)-F_{\mathrm{R}}(p)=T_{\mathrm{R}}\,D_{\mathrm{KL}}(q\Vert p)$; the entropy-maximization steps are classical once the cost is fixed. New technical content includes a non-asymptotic Stirling bound and soft-shell constrained-type theorems for real-valued costs. A three-state example compares the Gibbs law to squared-log, affinity-as-energy, and Tsallis alternatives at the same cost vector and mean-cost constraint, with sample-size power calculations at fixed RCL ground truth. The framework is conditional on axioms (A1)--(A3) and restricted to finite outcome spaces with strictly positive weights; it does not derive the composition law from a more primitive principle.
arXiv:2605.16239v1 Announce Type: new
Abstract: We introduce a dynamics-level approach to watermarking generative models. Rather than embedding signals into model weights or outputs, we embed the watermark directly into the learned continuous dynamics -- the velocity field of a flow matching model. We formulate this as random coding over a continuous channel: a key-dependent perturbation is added during training, and the message is recovered at detection time from black-box queries. The perturbation is designed to leave the generated distribution unchanged. Experiments on MNIST and CIFAR-10 across different architectures confirm reliable message recovery, preserved generation quality, and chance-level decoding accuracy without the secret key.
arXiv:2605.08464v2 Announce Type: replace
Abstract: The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the training data provides a sufficiently dense sample of the underlying low-dimensional data manifold, or where such a low-dimensional manifold is conceivably present. We describe the regimes where the MH is not applicable as sparse. In this paper, we demonstrate that models succeed in the sparse regime by exploiting a highly structured local geometry, a property we formalize as normal alignment. We prove that normal-aligned classifiers -- whose input-output Jacobians are rank-one and align perfectly with the training data -- minimize the training objective under norm constraints and achieve maximal local robustness under a non-zero Jacobian constraint. For continuous piecewise-affine deep networks, normal alignment manifests geometrically as centroid alignment within the network's induced power diagram partition and results from the feature-learning regime. Motivated by these theoretical insights, we introduce GrokAlign, a regularization strategy that actively induces normal alignment. We demonstrate that GrokAlign significantly accelerates the training dynamics of deep networks relevant to the grokking phenomenon. Furthermore, we apply the principle of normal alignment to Recursive Feature Machines (RFMs) to introduce Recursive Feature Alignment Machines (RFAMs). We show that RFAMs exhibit greater adversarial robustness compared to RFMs when trained on tabular data.
arXiv:2605.16241v1 Announce Type: new
Abstract: Billion-parameter Vision-Language-Action (VLA) policies have recently shown impressive performance in robotic manipulation, yet their size and inference cost remain major obstacles for real-time closed-loop control. We introduce \textbf{VLA-AD}, a distillation framework that uses a Vision-Language Model as an offline semantic supervisor to transfer large VLA teachers into lightweight student policies. Instead of relying only on low-level action imitation, VLA-AD augments teacher-provided 7-DoF action targets with high-level semantic guidance, including task phase anchors and multi-frame operating-direction descriptions. These auxiliary signals are used only during training: at test time, the student policy runs independently, with neither the VLA teacher nor the VLM required. We evaluate VLA-AD on three LIBERO benchmark suites. Using OpenVLA-7B as the teacher, our method produces a 158M-parameter student, yielding a $44\times$ reduction in model size while matching the teacher with only a $0.27\%$ average relative gap. The resulting policy runs at 12.5 Hz on an RTX 4090, achieving a $3.28\times$ inference speedup over OpenVLA-7B. We further show that the same semantic distillation pipeline generalizes to a different $\pi_{0.5}$-4B teacher, where the student outperforms the teacher on two suites and remains within $0.53\%$ on \texttt{libero\_goal}. Additional analysis indicates that phase-level supervision and multi-frame directional cues make the student less sensitive to noisy teacher actions, such as erroneous high-frequency gripper changes. Overall, VLA-AD demonstrates that offline semantic guidance from VLMs can substantially improve the efficiency, robustness, and deployability of VLA policy distillation.
arXiv:2605.16227v1 Announce Type: new
Abstract: Deep Neural Networks (DNNs) are high-value intellectual property (IP), yet deploying them to edge environments exposes them to \textbf{unrestricted oracle access}, rendering them vulnerable to model extraction and inversion attacks. Existing defenses fail to address this practically: passive watermarking only offers post-hoc provenance, while active defenses impose prohibitive latency or require persistent access to sensitive training data. To bridge this gap, we propose \textit{LymphNode}, a novel post-hoc defense framework that acts as an intrinsic ``immune system" within the model. \textit{LymphNode} enforces a strict ``default-deny'' policy: it actively neutralizes model utility for unauthorized queries via \textbf{Generalized Sparse Universal Adversarial Perturbations (GSUAP)} injected into the feature space, effectively blocking gradient estimation and data inference. Utility is selectively restored only for authorized inputs carrying a stealthy feature-domain credential. Our framework is highly practical: it is \textbf{data-efficient}, establishing robust protection with fewer than 100 samples ($<1\%$ of training data), and \textbf{cross-dataset adaptable}, enabling protection using public surrogate datasets. \textit{LymphNode} thus provides a lightweight, immediately deployable defense for high-stakes scenarios where original training data is restricted or unavailable.
arXiv:2605.16225v1 Announce Type: new
Abstract: The study of optimal preemption policies for status update systems has been a recurring topic in the age of information (AoI) literature, where threshold-based structures have been shown to be optimal under a generate-at-will update generation model under certain assumptions. In this work, we study the effectiveness of threshold-based policies for a system with random update arrivals. In this regard, we introduce an analytical framework for evaluating the AoI of multi-threshold preemption policies and present interesting characteristics of the structure of the optimal preemption policy. We show the effectiveness of these threshold-based policies over the traditional probabilistic preemption policies and single-threshold policies, where we observe that significant gains in terms of AoI can be obtained by utilizing both the age of the packet and the age of the system when designing these preemption policies.
arXiv:2605.16222v1 Announce Type: new
Abstract: Aphasias, selective language impairments which can arise from brain damage, reveal the functional organization of human language by providing causal links between affected brain regions and specific symptom profiles. Drawing on this literature, we introduce an aphasia-inspired technique to characterize the emergent functional organization of language models (LMs). We ``lesion'' (zero-out) model parameters and measure the effects of this intervention against clinical aphasia symptoms, as diagnosed by the Text Aphasia Battery (TAB). When applied to 112,426 outputs from five 1B-scale LMs, the full range of evaluated symptoms surface, but in distributions largely distinct from those of humans. Our method uncovers broad symptom-profile differences between attention components (query, key, value, output) and feed-forward components (up, gate, down), with weaker evidence for differences among components within the same mechanism. We also find an effect of depth, where lesions in early layers disproportionately cause syntactic and semantic symptoms while late-middle layers yield higher rates of phonological and fluency deficits. Although some LM lesions induce quantitatively more similar profiles to some human aphasia types than others, qualitative differences in symptom patterns between LMs and humans suggest that aphasia syndromes are heavily influenced by the details of learning and processing rather than being a domain-invariant consequence of disrupted language processing.
arXiv:2605.16219v1 Announce Type: new
Abstract: Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\tau$, the privacy-relevant sample size is not $n$, but $n\tau$; equivalently, the effective private tail sample size is $\epsilon n\tau$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $\Theta(B \min\{1,(n\tau)^{-1/2}+(\epsilon n\tau)^{-1}\})$, and finite classes of size $M$ have rate $\Theta(B \min\{1,\sqrt{\log(2M)/(n\tau)}+\log(2M)/(\epsilon n\tau)\})$. These complete rates hold under pure DP, and their lower bounds extend to approximate DP in the stated small-$\delta$ regimes. For convex Lipschitz learning, modular upper and lower reductions show that the CVaR-specific privacy term necessarily scales as $1/(\epsilon n\tau)$, with dimension dependence inherited from private stochastic convex optimization. Together, these results identify ordinary private learning on $\Theta(n\tau)$ informative tail records as the canonical hard subproblem inside private CVaR learning.
arXiv:2505.24364v2 Announce Type: replace
Abstract: A key concept for many graph layout algorithms is planarity, a graph property that allows to draw vertices and edges crossing-free in the plane. Important is the generalization to $k$-planar graphs, which can be drawn in the plane with at most $k > 0$ crossings per edge. One of the basic graph properties that have been explored for those graph classes is the maximum edge density, i.e., the maximum number of edges a $k$-planar graph on $n$ vertices may have. While there are numerous results for the classes of $1$- and $2$-planar graphs, there are few results for increasing $k=3$ or $4$ due to the complex graph structures. We make a first step towards even larger $k>4$ exploring the class of $5$-planar graphs. While our main tool is still a discharging technique, a better understanding of the structure of the denser parts leads to corresponding density bounds in a much simpler way. We first apply a simplified version of our technique to outer $5$-planar graphs and surprisingly observe that the structure of maximally dense (general) $5$-planar graphs differs from the known uniform structure of maximally dense $k$-planar graphs for smaller $1 \leq k \leq 4$. As the central result of this paper, we then show that graphs that admit a simple 5-planar drawing have at most $7(n-2)$ edges, drastically improving the previous best bound of $\approx8.3n$. This even implies a small improvement of the leading constant in the Crossing Lemma $cr(G) \ge c \frac{m^3}{n^2}$ from $c=\frac{1}{27.48}$ to $c=\frac{1}{27.3}$. To demonstrate the potential of our new technique, we also apply it to 4-planar and 6-planar graphs.
arXiv:2605.16213v1 Announce Type: new
Abstract: Sorting is a fundamental operation across numerous computational domains. Traditionally, this process involves transferring data from main memory to a processing unit for sorting, followed by writing the sorted data back to memory. This conventional approach incurs substantial latency and energy overheads due to the extensive data movement between memory and processing components. To mitigate these overheads, this paper introduces novel architectures for executing sorting operations directly within the memory fabric, eliminating the need for off-chip data transfer. To our knowledge, this work represents the first exploration of in-memory sorting using 6T SRAM. The proposed architecture is designed to operate on data represented in the standard weighted binary radix format commonly used in digital systems. The proposed architecture achieves a significant 3.4x reduction in latency compared to memristor-based IMC sorting.